Calculating Power consumption

I know this is a total N00b question, but I can't really understand how to calculate the battery usage of my arduino and all the electronics connected to it.
I know I'm supposed to look at the data sheets, but what am I looking for and how can I apply that to what type of battery to use?

I guess that's where I'm really confused, when should I not connect something to the arduino power (in favor of a dedicated power supply) and how can I figure what type of battery to implement?

Does this make sense?

I think you might mean current consumption not power consumption.

I know I'm supposed to look at the data sheets,

Yes it depends on what the circuit is.
A raw arduino allow about 50mA for, then if you have say 6 LEDs at 20mA each then that is 120mA making a total of 170mA.

Depending on the capacity of your battery you can work out how long it will last. So say for a 500mA/h battery this will last (very approximately)
500 / 120 = 4 hours.

If you have a multimeter with a mA selection you could also measure the current draw and get a good idea of how much you are using as well. You will need to be able to insert your probes in series with the power source and the 'Vin' pin if using the regular or VCC/+5V pin if you are running off batteries directly (say from 3 AAs for example).
You are bypassing the reverse protection diode this way, so make sure you have ground connected to ground, or ground to battery-.

If you don't have a multimeter, pick one up. It will be an invaluable tool.

Roughly speaking, a battery rated 2000mAH will provide 2000 mA for one hour, or 1000mA for 2 hours, or 500mA for 4 hours, and so on. Connecting batteries in series gets you a higher voltage, but does not increase the mAH rating, while connecting batteries in parallel increases mAH, but not voltage.

So a "typical" microcontroller battery of 4 1500 mAH NiMH cells connected in series (to give approximately 5V, wired to 5V in) will still be 1500mAH and would power a bare arduino board (about 50mA) for 30 hours.

If you have a circuit built, you're probably as well off measuring its current draw as you would be reading datasheets.

BillW

This is an amazing community - I've been really enjoying learning all this. I don't have any one project this is for, but I'm one of those 'peer down the road' type of people and was curious about how all the power consumption stuff is considered. I know I was missing it, but it helps to know the arduino draws 50mA and the rest can come from data sheets.

I do have a multi-meter, but am a bit confused on 'CrossRoads' example of where to put the probes. Wouldn't I just put the positive in the 5.5v pin and the ground in the ground? Does this need to be done with the power supplied or will that mess up the multi-meter's calculation?

For my example, you would replace the wire from the battery+ (for example) to the Vin pin, assuming you were using a 9V battery and the onboard regulator.
If you were using 3 AAs instead, then the meter would go between battery+ and the Vcc/5V pin.
Your example of +5 to Gnd would be good for measuring voltage, with the meter in parallel with the ciruit. My example is making the meter part of the circuit, part of the actual wiring, for measuring current flow.

Wouldn't I just put the positive in the 5.5v pin and the ground in the ground?

And then putting the meter into current mode is why God invented fuses inside multimeters.

@biscuitcleaver,
You can measure between the 5.5V and ground if you are measuring voltage using the DV Volts setting on your meter.
If you want to measure current, to need to insert your meter between the 5V source and the 5V connection of your circuit so you can see how much current is going into your circuit, you would do that with the mA setting on your meter.